Evolution is one of the most important dynamic processes in studing complex systems. The species are interconnected in each population and their relationship shows population structure. The process of evolution of new species in the population is one of the most important matter in evolution. Unless a mutation occurs in a fixed population of two species with different reproduction rate (fitness), one species dominantes and stabilizes the population. The probability of this event is presented as the fixation probability and the time it occurs with the average fixation time. population structure has an impact on the fixation process. So far much research has been done to identify the populations that have maximum fixation probability, but these amplifier graphs typically increase the fixation time. This study examines the population structures that are exchanged between fixation probability and average fixation time. In fact, we look at population structures that significantly increase their probability of fixation with a small increase in average fixation time. Using computer simulation in two large and small populations, we investigate the average fixation time and fixation probability of different graphs. The results show that the complete bipartite graphs have a probability of fixation near the star graph and average fixation time near the complete graph.